The present disclosure relates generally to systems and methods for processing data representing sigmoid or growth curves, and more particularly to systems and methods for determining characteristic cycle threshold (Ct) or elbow values in real-time Polymerase Chain Reaction (PCR) amplification curves, or elbow values in other growth curves.
The Polymerase Chain Reaction is an in vitro method for enzymatically synthesizing or amplifying defined nucleic acid sequences. The reaction typically uses two oligonucleotide primers that hybridize to opposite strands and flank a template or target DNA sequence that is to be amplified. Elongation of the primers is catalyzed by a heat-stable DNA polymerase. A repetitive series of cycles involving template denaturation, primer annealing, and extension of the annealed primers by the polymerase results in an exponential accumulation of a specific DNA fragment. Fluorescent probes or markers are typically used in the process to facilitate detection and quantification of the amplification process
A typical kinetic PCR curve is shown in FIG. 1A, where fluorescence intensity values are plotted vs. cycle number for a typical PCR process. In this case, the formation of PCR products is monitored in each cycle of the PCR process. The amplification is usually measured in thermocyclers which include components and devices for measuring fluorescence signals during the amplification reaction. An example of such a thermocycler is the Roche Diagnostics LightCycler (Cat. No. 20110468). The amplification products are, for example, detected by means of fluorescent labeled hybridization probes which only emit fluorescence signals when they are bound to the target nucleic acid or in certain cases also by means of fluorescent dyes that bind to double-stranded DNA.
For a typical PCR curve, identifying a transition point at the end of the baseline region, which is referred to commonly as the elbow value or cycle threshold (Ct) value, is extremely useful for understanding characteristics of the PCR amplification process. The Ct value may be used as a measure of efficiency of the PCR process. For example, typically a defined signal threshold is determined for all reactions to be analyzed and the number of cycles (Ct) required to reach this threshold value is determined for the target nucleic acid as well as for reference nucleic acids such as a standard or housekeeping gene. The absolute or relative copy numbers of the target molecule (starting material) can be determined on the basis of the Ct values obtained for the target nucleic acid and the reference nucleic acid (Gibson et al., Genome Research 6:995-1001; Bieche et al., Cancer Research 59:2759-2765, 1999; WO 97/46707; WO 97/46712; WO 97/46714). The elbow value 20 at the end of the baseline region 15 in FIG. 1A would be in the region of cycle number 30.
The elbow value in a PCR curve can be determined using several existing methods. For example, various methods determine the actual value of the elbow (Ct) as the value where the fluorescence on a normalized PCR curve reaches a predetermined signal level, called the AFL (arbitrary fluorescence value), which can be sensitive to changes in the average baseline fluorescent level in the pre-elbow PCR cycles. Other methods use the cycle number where the second derivative of fluorescence vs. cycle number reaches a maximum, which can give late Ct values, particularly for parabolic curves. Yet other methods use a tangent of the PCR curve at the inflection point (maximum of first derivative), which is problematic for parabolic curves as the maximum of the first derivative may not exist. (Guescini, BMC Bioinformatics, 9:326, 2008). Thus, the latter two methods both have drawbacks for parabolic curves. U.S. Pat. No. 8,219,366 solves the problem with parabolic curves by identifying such curves and using a different technique for such problematic curves. Although this method works well for qualitative real-time PCR, when applied to quantitative real-time PCR, it can lead to some increase in imprecision at low copy numbers.
Therefore it is desirable to provide systems and methods for determining Ct value in growth curves, such as real-time PCR amplification curves or other growth curves, which overcome the above and other problems.